Question 21
Let $ABC$ be an acute triangle with $AC \gt AB$, and let $D$ be a point on $BC$ such that $AD = AB$ and $D$ is different from $B$. Let $\Gamma$ be the circumcircle of $ABC$, $\Delta$ the tangent to $\Gamma$ at $C$, and $E$ the intersection of $(AD)$ and $\Delta$.
Show that $CD^{2} = AD \cdot DE - BD \cdot DC$.
Show that $CD^{2} = AD \cdot DE - BD \cdot DC$.